GR03

33

description

gravitation

Transcript of GR03

  • !#"$%&('*)!,+.-//0'(21!,+34,5!36!7

    %859:!,;35?:!,.+@BACDAEE"F

  • 52833

    j5!,+@#7: %!,68O5+fF5%#aC]:;

    !,AC'

    %5:5V5

    mG!r7f>+ m4]#

    ::

    +3DAV!,:55!+@5%8

    !&%1!,3.AC+!,rA?rT!,+@gD@A3+35+3#+@F5:3%8G!,AC+@2+39

    +3

    8! 5 3!&2rA4]+3fa&5%!,,52

    /

    0

    z 93%~

    =F!,m1+ 6%

    mC

    + 2#@%!, AC+37,rr:7rT,!+@y8!&F,A,;m1!&%

    &55!(:5+3*%%5]#8!!&m1+ '8!*!r],52* $e$:g

    %A 5

    ( @

    >1!4A+n!,f8!,{r&5%5!r5

    AC!78:C5+3 +@x,52O5+@X+@ f:+ +3ACACG%85 %!&% !&xACr!+3#!

    +,5#%!+@3+43!&2,A}, AC,!,+]>5

    +3 %8

    5#D!,7a!7,+3#,5

    +3(DA,5275

    , 8!, AC+@r%!& %5!

    !%!&AC3, 8

    52,1!,a!&5%!,g+@!!,+rA.;5 !7,+3

    5f7 %+3

    !j!&&+35+@>+@ 7 +3

    ;G,5 iX!,+3+33#%8op f:+12'%A

    AC!,2+@36+33:7!&2,A9?+@T,:!+36pO+7+9,!+3;5B

    r:!,y,54!,m1+,9!

    +3 8!&?++@AC?8!, 8|%33+ 3122,!r< 8 : 5m16CAE !, 8!

    3T,!%+@ :

    +3!,+HF5%5!+@ 7 +3

    +3@%!,+ , 5#%+3

    N

  • %8>%:y!&%78!,2+3j8$,51rT,!#]%f+@% +(,541rT,!,+3O%

    # 7:!rAB]%:F5,!, 8!%+3

    *

    z&]~

    *

    z]~

    "

    z&]~ zw-/~

    rm1F,55C7+@ :&5rA}'(19+8G,58:T+3

    +@g&5%!,+,!,!+3354f:%+3952gAC!, +#,54!,m1+,2,+%k]%,f+@%X+@gf:2,+98!g

    %!+@:@%!g+%+3%8o5#5fC+3%3!,3126f:,+,+r

    7

    ;

    ' 3

    7

    7

    7

    0!

    F

    K zw-%0f~

    5!,

    F

    AC%r>5# A+ 5+@+@ ik+@( $f:%+3'AV+j 3,

    5 5a

    ,+@% 5!,< =>5+34%!+@:@%!

    mK8F3+%4+

    +3 !,:!

    5

    .pX+37+3 #f:%+3@2,!#

  • =>5?]+3fV%8#,59)Cr+@%@2,+1+ ,5! +@BB,52;7+3

    +3B8:!VAC+@!

    +%b52

    63V8!,%2g< =,%+@A y3+'+3

    +3'!

    +35f3+3jz|:Q~o%A#5G+f&oT,A#,5$1!o%!,$,%+@AF]G%k3+'

    +3

    +3'$! +35f3+3;7%!&2,+< :!1V+@,%+@A]67+3'x+3 3+;!

    +35f3+3 +8>+,&%f#1!,%!, %

    mC7+3'%

    mCj+3 3+'*!#%

    mC

    +35f3+3

  • =>5#%,+V8k7!&%+35f3+ Afr>% !,3BACA5#%,+8o3%5('%A

    +3 !,+3 +%8:+3..+3

    +!&A!

    +?

    5+3&5 7: 2,+K21!g+!& 8 !r2,A+3AC+@r'xB: &%+3!,%AK

    AC

    7,%+3!&'C%!,1!

    !,+C+@+35#!r%}:g]!&

    (

    7

    %!,F

    ;G,5

    ]f,k%8]5 1rT!k!3%+31F+317+@+,8k

    (

    7

    '

    +,55 &5+3%8k+3>:AC!&7CA},!,78!, %+3

    7

    *+

    7-,

    I +

    7-,

    ;.

    ;

    7

    ,

    0

    z Hf-~

    =>5 1!,j571#AC; &5%

    557+@F+3#&5%+'7,;$!

    %,5 &5%F+;7+@G5 ]&>g:7a&5jI

    (

    7

    (

    7

    ,

    7

    ,

    ;

    (

    ;

    z HH~

    5!,

    +3 2,!+}52

    .

    ;

    7/,

    7

    ,

    =

    ;

    =

    0

    z H$N~

    2

    .

    A

    %!,jr&5%,5!r >+31!,+1f(A

    7 ;

    8!O!&% -'A

    75 !&%78!,2+3?!!7,+rF%8O,5

    212%!,+3f7!,o%!,G+31gf,5G!&%78!,2,+#!!7,+r(8,5Gf!&m12%!,+3f

    r8*,5 :!1>%!I

    4

    7 ;

    7

    4

    ;

    4

    4

    7 ;

    7

    ;

    4

    4

    z&0f~

    7 ;

    7

    ;

    0

    ) :! ACD++3;%8o5#%,5V8k :!1F+@CAVAD++3(+

    ]+3&

    %A

    8

    +3X5%$:!,1

    7

    z~x,52$!,$!

    +3HrG5#+3f!,xz&m~T5.:;:g!,+3&5 %!&% ,!+3H%+3B8k5:!,1#+@ 8|%!a!+,!,!

  • %A4%8Q!Gg%!+@%]+f,!&2,+4%AB7

    a+@AC+y:

    aDA ,52G5+3G12%+@5$+8

    %AV3B+8

    7 ;

    q

    ;

    "

    -

    z

    ;

    7 =

    "#

    =

    7 ; ,

    7

    ;:=

    ~

    ;

    =

    /

    0

    z 3?H~

    =>5+3+@F5fZ&WZTRTN|u;ZY^%SwN|W%[< +31!,.+ ]!,r'(

    !++ %+3'

    +5;F+3ACV!&%+@7rA}I

    q

    7

    "

    -

    7

    z

    ;

    =

    "#

    =

    ; ,

    ;:=

    ~

    ;

    =

    /

    0

    z 320f~

    4+31y,5;!,% :7:%3,5675!7 %5 ]

    +f&+3 5%G+1rT!$'+3$52>1!,

    %!,G 21Ayf 5 AC+n !5+35%X%x%!,O,5+3!O f,x5:A

    %!,:A'5!43; 21A?6.%,5! ,%f '*+7+3621!#%%5!

    +fa+35 +83A5 +;]+3 +@,5 ,% 5:5('% B5%

    0

    +3 ,3!$8:T,+I

    ,

    0

    ,

    z

    4

    ~

    ,

    ,

    0

    z&]~

    0

    z&]~

    0

    z&]~

    0

    z 3%~

    e$21m!+@%fr'*f!&m1m!+@%fr'*%A

    +CA,! 5+5!y!,C!&% 8! +,5

    m ,52a5:3A4

    #f1+3:5!&%3+Hr2,+g, %!,+,!,!#!&%g75:@A 1f+3:f

    52

    +@ ,%@%!r5!,8!'+B++,H!,:3'

    z

    ~

    "

    0

    z|3%~

    "$:

    5m1 %3!rAC.!,A.5%F,5 8Q 5%A?+3AC 5! ]

    !+7,%

    !&AC+%!, !&A+r< )'

    !++3 :CB,5212%!,+3BA!,+122,+16%8#,5212%!,+3

    1!>A;28Q,!

    !,AG!,!!&%+#!'

    #

    z

    ,

    "

    ~

    /

    0

    z|~

    =>5+3 g:7,!:8! %3&5+@r>%8

    5!,8!

    ,

    0

    z|~

    j 6&5&B5% 5+@,!,78!, >3+3g21m!+@%f>!r

  • !r'

    !+7,; !,j+@+3

    z

    A

    "

    !

    A

    ~

    A

    zoz~~

    "

    !

    z&*z~7~

    A

    z&*z~7~

    /

    0

    z|f-~

    =>5+3F+@V%8$:rA6!&AC+3%!,z|Ff7rA.,V!7,+3@~aAC+n]!,+3kf:2,+

    %AV+83

    G525!,F+@ :+ f: 3:C+3V8! A

    z*z~7~5% +3G,4m'

    af4 ?FT,+4+31r$y:+ f:!,,!,+C,+8!G!,3!&%]!$%8

    1rT,!%3 r+DA%5 a]+3f 5!,

    +3]Ff:!1B

    z~

    5j,%fG1!,G2

    :%5#+31V1rT! +

    %

    A

    0

    z|~

    5

    %?7'}+@j5! V:!,1

    z~F7:&5?5%j,5%]21y+3j!,:'%A7:&5

    5%G+8

    a!,3!&%7]!BA

    %3#5#:!1 ,5B51rT,!X,52!,:,

    +3

    %!,

    +,5K,5,%f1!%1!,+f%3?5;:!1 L =>5Cf:7+3

    rAG,4%f:2,+I

    8

    8

    "

    !

    /CK z //~

    +,5 5+3++@%#AC++3 zwf~T< =>5+@B+@; A !,AC!V!,A+!EAC+n]!f+@%

    f:2,+8!

    z~T'%A;+j

    mC>5j7:C,+KzQ8!a7 !,8~],7+33F:!1a,5!,:5 +3V5#AC+3!rT,+B%8

    A

    '%A.+3%3rA6BCACr7+@

    +5?!,]TFB5 9? rT+3(

  • =>5 38Qj5%A.+3A +3j7!jACAC+343+%!,3B A

    '] 5!,8!, )

    !

    +@a

    7!' !, +3z r/-~T'%#z r/!Hf~T5 A+3AC!

    K

    /5f++@ACf+ 4:

    +,51rT,!G8!G5 AC!,+12%+31$, T

    5OD!,7*,5!,Gf:2,+*+ 3#52o5>:g]!k8%3!,+3%3F+3AC]ACf

    ]f,#8$,5B+3%,!#+@ .z+3

    6A+ 7+3&~T'o7+ z|+,5!,r~'

    !

    f 9z+3.8:!FAC+3

    +,~< =>5g!,75+@ 5]j+3j 83

    I$(a,5

    AC+ 7+3E] $x< "G%:;%8j ]

  • +3

    E,5 uYCPTcm^%SwYCPZ;Ru&^%_^2PT< a%,5!47!%8j+3f!r +@ 5>NQ[RTSZNQ[

    SZ[RW2P

    )

    ,

    -

    )

    0

    z r/~

    =>5+3F!7,+3:@%!jy+2+3?+3F+3

    ]!,fj]:g,5"G+@%&5+*+@ACf,+,+rj+3 3

    5%

    /

    0

    z r~

    &>+&

    ]%:+ C:!&>+.pX+37+ GD3Af:%+3#zw

    +3(r~

    rG!j%8k:!,

    %>'

    5!, ,5

    !,+3 7!F% &56+AC]Af#%8X,5f!,A+%r5B5 e$5!,+37n]]g]@$! H!,'%AV7y+3O5F+34,!r%8o5 +3+},!%!,

    )

    ,

    4 4

    )

    ,

    4 4

    z N~

    %ABD34,5 :!,122,:!#,3!G+@

    -3

  • )

    ,

    -

    4 4

    0

    z ~

    aT,:%33'}+3?

    VAC+3 +3 A63.+?

    AC+ 7+3'

    5!y5!,y+@F3

    ;+3AC]ACfB f4%8j56 + 7!

    .% C!,,g,5;8:3

    +%!8:T+3;8>)I

    )

    -

    ) z&

    ,

    ~

    0

    z 93%~

    z|=>5V!+35f 5AK+3ACB5 54!,+35fg+3ACf ,!+3y%A:K%K&5r&652

    )

    )< ~.

    BAC+3 +3'*5g+C8!%+36%]:F:!122,:!, +3a+?

    8:T,+'C,5 %@%!:!122,:!,